Non-linear elements give rise to disturbances in the form of harmonics in the power networks to which they are connected. Thus, for example, by its operating principle comprising the cyclic connections of different parts of the alternating voltage via the valves included in the convertor, a convertor connected to an a.c. network generates harmonic currents on its a.c. side and harmonic voltages on its d.c. side. During the time intervals between the commutations, however, the convertor may be regarded as a linear element and the currents and voltages arising in the power network may therefore, during the above-mentioned time intervals, be determined from a linear model based on the knowledge of the phase position and the amplitude of the applied voltage as well as on the impedance and initial state of the network. Further, the cyclic connections impart to the currents and voltages arising waveforms which, during a steady state, are repeated for the respective time interval. In principle, only harmonics of the order n=kp .+-.1 occur on the a.c. side and of the order n=kp on the d.c. side, where p is the pulse number of the converter and k is a positive integer.
To reduce the stresses, originating from the harmonics, on the components included in the power network and to fulfill the requirements made on the effect of the harmonics on the network, therefore, filters are generally required to limit the propagation of the disturbances in the power network. Especially in plants for transformation between alternating current and high-voltage direct current, where there are also placed demands for limitation of telecommunications disturbances emanating from the lines, extensive installations for filtering the generated harmonics are required. These filters are generally built up from passive components and are tuned to the harmonics of a lower order whereas the harmonics of a higher order are filtered through a high-pass filter. When calculating the passive filters, factors such as resonances with the impedance of the network--which impedance is dependent on the network configuration--are also taken into account. The fact that the passive filters, installed on the a.c. side, are also to serve as members for generating reactive power is also taken into account.
Drift at mains frequency and in component values means that an exact tuning generally cannot be maintained, and also at the resonance frequency the filter impedance will not always be negligible as compared to the network impedance. In practice, therefore, harmonics remain in the network and to this is to be added the fact that during the actual commutations and due to any phase unsymmetries, harmonics of other numbers of order than those mentioned above are also normally generated.
The above-mentioned limitations of the passive filters have therefore led to proposals for the use of active filters instead, whereby the network via these filters are supplied with currents or voltages counteracting those which are generated by the disturbance source. By measuring the remaining harmonic contents in the power network, the supplied currents or voltages can then, in principle, be given such waveforms that they completely eliminate the harmonic contents of the network. Thus, in the IEEE publication 89 WM 123-1 PWRD (IEEE/PES 1989 Winter Meeting, New York 1989): Cheuksum Wong, Ned Mohan, Selwyn E. Wright and Karl N. Mortensen: Feasibility Study of AC- and DC-Side Active Filters for HVDC Converter Terminals, there is given a technical and economic evaluation of a device comprising a controllable current generator which is intended to be connected between line and ground in an HVDC station. The evaluation is based on calculations and on simulations of the device connected to the direct voltage side. The results indicate a good technical effect, but as far as is clear from the report the simulations have been performed only for steady state while considering harmonics of the orders 12, 24 and 36. Further, a greatly simplified model of the converter has been used and the effect of the direct voltage line has been neglected. By this approach it has been possible to calculate, based on the model, the reference value of the current which, via the current generator, is to be supplied to the network to eliminate the harmonics considered, and this reference value has then been used during the simulations. The report indicates a method of controlling the current generator of the active filter by harmonic analysis of the direct voltage at the converter and, by feedback via PI regulators, forming a reference value for the current generator such that the contents of harmonics of the above-mentioned three orders in the direct voltage are controlled towards zero.
As mentioned above, the connected power network shows an impedance with several resonance frequencies, and in fact, in view of the complicated characteristics in the frequency domain of an extended power network, control systems based only on feedback are likely to involve difficult dimensioning problems.
Essentially, the control problem is caused by the non-minimum phase behavior of the transfer functions of the electric power network. The physical reason for this behavior are electromagnetic waves travelling along the power lines and their reflections at points with changes in the impedance characteristics. This implies multiple transportation delay effects (echoes) on control responses of the electric power network as the natural damping effect on travelling waves is very low.
It is well known from text books in control theory, for example Bernard Friedland, Control System Design, McGraw-Hill International Editions, 1987, ISBN 0-07-100420-3, pp. 78, 144, 188, note 4.7, and Richard C. Dorf, Modern Control Systems, Addison-Wesley Publishing Company, Fourth Edition, 1986, ISBN 0-201-05326-8, pp. 262-264, that non-minimum phase implies zeros in the righthand part of the complex s-plane and it is also impossible to make stable feedback control with very quick response for non-minimum phase systems.
The need to reduce disturbances with a certain frequency content also exists in other physical processes, and methods for this have also been published on several occasions. Thus, PCT application PCT/GB80/00128 (WO 81/00638) discloses a method for reduction of acoustic disturbances, or more generally vibrations in gases, liquids, or solids, in which the periodic character of a disturbance source is utilized in such a way that a signal stored in a memory member is applied, repetitively and synchronized from the disturbance source, to a loudspeaker placed at a location where the disturbance is to be reduced. The acoustic pressure generated by the loudspeaker is given such an amplitude and such a phase position that it tends to extinguish the original disturbance. The desired cancellation of the disturbance is thereby obtained in such a way that the resultant acoustic pressure is sensed by a microphone whereupon, after certain signal processing, the signal stored in the memory member is corrected in such a way that it tends to further reduce the resultant acoustic pressure. Specifically, the last-mentioned publication describes methods whereby the correction is calculated from a measured value synchronized with the disturbance source and is added to the contents of the memory member in a phase-correct manner in view of the acoustic delay of the system, whereby the magnitude of the correction can either be given predetermined values or be in proportion to the amplitude of the resultant acoustic pressure.
Also EP application No. 88112057.0 (Publ. No. 0 301 483) describes a controller for a power convertor for systems for non-interrupted power supply, active filters, etc. The controller comprises a memory member adapted to store a signal corresponding to the output signal of the controller during a period of a repetitive sequence. The signal stored in the memory member is corrected by adding the control error, with one cycle's time delay, to the contents of the memory.
The introduction of a memory member for storage of signal values in the controller makes it possible to achieve a good cancellation of a stationary periodic disturbance, also with an amplification in the feedback loop which is low for reasons of stability. However, a low amplification means that the contents of the memory member is corrected relatively slowly during non-steady states.
The major disadvantage in this case is that delay effects and other non-minimum phase effects as well as other types of system dynamics are not included and compensated. In general, the correction of the memory with the control error delayed one period will make the controller unstable as there are implicit or explicit delay effects of the systems and other dynamics as well. The total delays add up to more than one period and therefore, even if the controlled system is stable, the damping effect of disturbances with one period repetitive patterns is not very high.